Protein folding studied using a two-dimensional lattice model with the Hamiltonian including both hydrophobic interactions and main chain hydrogen bond interactions of amino acids. Since compact conformations have different designabilities and only highly designable conformations can act as native structural candidates [H. Li, R. Helling, C. Tang, and N. Wingreen, Science 273, 666 (1996)], it is shown that hydrophobic interaction alone is insufficient to explain the appearance of a high proportion of regular secondary structures, especially beta sheets whose content decreases with increasing designability, but interactions of main chain hydrogen bonds can account for this. Thus the emergence of only a small number of structure types (folds) among all possible structures can be understood to some extent.